Multiple choice

Directions: Select the correct alternative from the given choices. If A starts a work, completes one-third of it and hands it over to B to complete the remaining work, it would take 40 days for the work be completed. Instead, if B first completes one-third of the work and then A takes over and completes the remaining work, it would take 35 days for the work to be completed. In how many day can A and B together complete the entire work?

  1. 16

  2. 24

  3. 18

  4. 20
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A and B take x and y days to complete the work. (1/3)x + (2/3)y = 40 and (2/3)x + (1/3)y = 35. Multiply by 3: x + 2y = 120 and 2x + y = 105. Solving gives x=30, y=45. Together: 1/(1/30 + 1/45) = 1/(3/90 + 2/90) = 90/5 = 18 days.

AI explanation

Let A complete the work in x days and B complete the work in y days. Based on the conditions, we get (x/3) + (2y/3) = 40 and (y/3) + (2x/3) = 35. Multiplying by 3 gives x + 2y = 120 and 2x + y = 105; adding these equations yields 3x + 3y = 225, so x + y = 75. The time taken by A and B together is found by dividing the product of their times by their sum, xy/(x + y), but here we can use the harmonic mean relation for combined work where 1/T = 1/x + 1/y. Since x + y = 75 and xy = 1350, their combined time T is 1350 / 75 = 18 days.

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